They kept the Chiefs tryless in a match which looked set to be decided by a kicking battle between Damian McKenzie for the Chiefs and the Blues' playmaker Otere Black.
But two well-taken tries proved pivotal, and the Blues eased to the top of the Super Rugby Aotearoa ladder with their first win over the Chiefs in Hamilton since 2011.
The Chiefs drew first blood with a McKenzie penalty after 12 minutes, only for the Blues to hit back two minutes later when No.8 Hoskins Sotutu powered over from close range after a solid Blues lineout.
Another McKenzie penalty kept the Chiefs in touch as the penalties against the Blues mounted steadily.
Black's 37th minute penalty pushed the Chiefs' lead out to 10-6, but the Blues were reduced to 14 men two minutes later when flanker Dalton Papali'i was yellow carded.
McKenzie nailed the penalty, and the Blues took a 10-9 lead into the break.
The Blues survived Papali'i's absence without conceding further points, but the battle of the boot continued with McKenzie and Black trading penalties to give the Blues a 13-12 lead as the hour mark ticked over.
Beauden Barrett's 64th minute drop goal extended the Blues lead to 16-12, with the All Blacks playmaker nailing another penalty four minutes later to push the margin out to seven points.
The Blues switched up a gear going into the final 10 minutes, swinging the ball wide to left and right before wing Mark Telea dived over in the corner to put the game beyond doubt.
The Blues have now won their last six games, including a 30-20 victory over the Hurricanes in their first game of the new competition last week.
In contrast, the Chiefs are winless after two games, tonight's defeat following last week's 28-27 loss to the Highlanders in Dunedin.